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Computer Science > Programming Languages

Title:
Elaborating Intersection and Union Types

Abstract: Designing and implementing typed programming languages is hard. Every new
type system feature requires extending the metatheory and implementation, which
are often complicated and fragile. To ease this process, we would like to
provide general mechanisms that subsume many different features.
In modern type systems, parametric polymorphism is fundamental, but
intersection polymorphism has gained little traction in programming languages.
Most practical intersection type systems have supported only refinement
intersections, which increase the expressiveness of types (more precise
properties can be checked) without altering the expressiveness of terms;
refinement intersections can simply be erased during compilation. In contrast,
unrestricted intersections increase the expressiveness of terms, and can be
used to encode diverse language features, promising an economy of both theory
and implementation.
We describe a foundation for compiling unrestricted intersection and union
types: an elaboration type system that generates ordinary lambda-calculus
terms. The key feature is a Forsythe-like merge construct. With this construct,
not all reductions of the source program preserve types; however, we prove that
ordinary call-by-value evaluation of the elaborated program corresponds to a
type-preserving evaluation of the source program.
We also describe a prototype implementation and applications of unrestricted
intersections and unions: records, operator overloading, and simulating dynamic
typing.